Respec is slang for respecialisation and refers to a game feature that allows players to partially or completely reallocate the points they have spent in various skills, 'talents', 'attributes', 'feats' or other character values. Respeccing in Diablo 3 will allow players to reallocate most or all of their skill points, thus allowing high level characters to change their play style.
This was not a feature offered in Diablo 1 or 2, where characters could never change their stat or skill points once they were placed. (Respecs were added to Diablo 2 in the v1.13 patch.)
Respecs are a player-friendly feature found in most RPGs, notably Blizzards MMORPG, World of WarCraft.
Diablo II Respecs
From Patch 1.13, Diablo 2 players can now respec.
Diablo III Respecs
Read more about Diablo III respecs in the main DiabloWiki: